\section{Basic Insurance Principles}
\label{sec:BasicInsurancePrinciples}

Insurance was practiced long before modern risk theory. Insurers must collect sufficient premiums to pay all their Claims Costs\index{Claims Costs} and non-claim related Operating Expenses\index{Operating Expenses}, reward policyholders or stockholders for using their capital (Profit Margin\index{Profit Margin}), and provide protection, the Risk Premium\index{Risk premium}, for their exposure to higher than expected Claims Costs (Hogg and Klugman, 1984; Bowers, Gerber, Hickman, Jones, and Nesbitt, 1997). Before issuing policies, insurer's have expectations about their revenues and costs, their Prospective Insurer Premium Allocation By Cost Components:

\begin{eqnarray} \label{eq:PremiumAllocationByCostsProspective}
\textrm{Premium Revenues} & = & \textrm{Claims Costs}\nonumber  \\
	&  & + \quad \textrm{Operating Expenses} \nonumber   \\
	&  & + \quad \textrm{Profit Margin} \nonumber  \\
	&  & + \quad \textrm{Risk Premium} 
\end{eqnarray}

Insurers' premium allocations are unknown until policies expire and accounting is complete. Claims Costs (Losses and Loss Adjustment Expenses) are usually insurers' highest and least certain costs. Insurers' Profits, Operating Losses, and Solvency are uncertain primarily because Claims Costs are uncertain. When all Claims Costs have been paid, when no uncertainty exists, there are no Profit Margins or Risk Premiums, just Profits or Operating Losses, the insurer's Retrospective Premium Allocation By Cost Components:

\begin{eqnarray} \label{eq:PremiumAllocationByCostsRetrospective}
\textrm{Profit (Operating Loss)} & = & \textrm{Premium Revenues} \nonumber \\
	&  & - \quad \textrm{Claims Costs}\nonumber  \\
	&  & - \quad \textrm{Operating Expenses} 
\end{eqnarray}
